The UN could strip Britain's statutory human rights body of its "A-list" status because of deep cuts by the coalition government, leaked documents disclose.

Letters between the home secretary, Theresa May, and senior UN officials show she has been warned that the Equality and Human Rights Commission would lose its financial autonomy – and consequently its UN rating – if cuts to its budget continued. This would mean the UK could no longer engage fully in the UN human rights council or work within the international co-ordinating committee. Countries with human rights organisations on the A-list include nearly all western European nations as well as Azerbaijan and Indonesia.

Those with "B-list" status include Kazakhstan, Sri Lanka and Congo-Brazzaville.

Any change in status within the UN would be deeply troubling to some senior Liberal Democrats who have voiced concerns over the way their coalition partners have slashed costs and undermined the influence of the commission. Last week, a bill passed through the Commons that will remove some of the commission's general duties including a commitment to support human rights and tackle discrimination.

In a letter sent on 28 June, the UN commissioner on human rights, Navanethem Pillay, warned May that the government's proposals should be reassessed because cuts threaten the independence of the body.

"I would like to call on your government to review some of the proposals with a view to preserving EHRC's independence and to ensuring its continued compliance with the principles relating to the status of national institutions," she said.

She went on the refer to the rules overseeing the commission's "A" rating and pointed out that Britain's statutory human rights body must retain financial autonomy.

If May was in any doubt over concerns within the UN, Dr Mousa Burayzat, chair of the international co-ordinating committee (ICC), sent her a second letter on 16 July, warning that the cuts raised serious concerns.

"While, if considered alone, the proposed legislative changes may not negatively impact on the Commission's 'A' accreditation, taken as a whole the package or proposals clearly constitutes a diminution of the EHRC's role and responsibilities.

"Whether this amounts to a threat to the A accreditation is a matter that only the ICC's sub-committee on accreditation can authoritatively advise following a systematic review," he said.

Burayzat, whose committee co-ordinates human rights organisations from across the world with support from the UN, criticised the government's decision to reduce the chairmanship from a full-time job to the equivalent of two days a week.

The commission has appointed Lady O'Neill as a part-time chairman to replace Trevor Phillips, whose term ended last month. May defended her decisions in a letter to Pillay. She blamed the commission for not keeping within its budget and said that its accounts had been questioned by the National Audit Office. She claimed the cuts were part of general government policy to reduce spending and insisted they had not compromised the commission's independence. She said the new chair will be a "strong and experienced leader" who will "have knowledge or experience of discrimination or human rights."

May's letter did not address the case for strengthening its independence or the need for stronger legislation to underpin this, nor propose any changes to the proposed cuts.

The coalition has set the commission a budget of £26.8m for 2014-15, a 62% cut to its 2007 budget of £70m. Insiders fear that the budget is likely to be cut to £18m.

Commenting on the letters, Chuka Umunna, the shadow business secretary, called for the government to drop plans to weaken the commission before they go before the House of Lords. "The United Nations writing to ministers to raise concerns over the potential downgrading of the EHRC is a very serious matter and should ring alarm bells for a government which has been accused of abolishing the EHRC by stealth by its own supporters," he said.

Institutions accredited by the UN with "A-list" status enjoy much greater access to UN human rights treaty bodies and other organs.

They can participate fully in the international and regional work and meetings of national institutions, as voting members. They are also able to participate in sessions of the Human Rights Council and take the floor under any agenda item, submit documentation and take up separate seating.

If reduced to "B" status, they participate as observers. They may not take the floor under agenda items or submit documentation to the Human Rights Council.

Oversight of the commission has been moved from the Home Office to the Department for Culture, Media and Sport. A DCMS spokeswoman said the government was reforming the commission because it had struggled to deliver across its wide remit, and hoped to retain its A rating. "That is why we are implementing a package of reforms to focus the EHRC on its core role as Great Britain's independent equality body and A-rated national human rights institution. Improvements have already been made," she said.